THEORY OF BINARY BOSON SOLUTIONS. Page: 8 of 30
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of this increased volume is the parameter a, defined as the fractional
increase in the volume of the system when a mass-4 particle8 is replaced
by a mass-3 particle. Measurements on He -He solutions give a Z 0.3
at zero pressure. Since a measure of the effective volume occupied by a
particle is liven approximately by the position of the first maximum in
the pair distribution function, and for pure liquid He4, the maximum of
9(44) (r) occurs at r0 - 3.4A, we expect g )(r) to exhibit a maximum
at (1 + a)1/3 r0 3.71. Hence, g (r) and g (r) are expected to
be quite different. The same is true for g(313)r). These differences
are allowed for in our present choice of the trial wavefunction.
In terms of s (r) and u (r), the expectation value of
the Hamiltonian can now be expressed as follows
(H) - (T) + <V) , (9)
where( ) - u ' ( ) ( ) d .
+ N3 9 u (43) r) 9 g(4,3)(r) dr]
+ [Nq u(,(r)-V 8(4,3) (r) dr
+ N3 j u (3,3)(r)-V 9(3'3)(r) dr] , (10)
V) = N r v(r) g 40(r) dr
+ H3 P4 jv(r) g(4,3 (r) dr
+ N3 3 v(r) g ((3'3 r) dr - (11)
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Massey, W.E. & Tan, H. THEORY OF BINARY BOSON SOLUTIONS., report, October 31, 1970; United States. (https://digital.library.unt.edu/ark:/67531/metadc1032575/m1/8/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.